Place Value & Partial Products
Multi-Digit Multiplication
Expressions & Parentheses
100

 Find the partial products and sum to compute 34 × 6 using partial products.

  • Answer: 34×6=(30×6)+(4×6)=180+24=20434×6=(30×6)+(4×6)=180+24=204
100

100 (100 pts): Multiply 23 × 15. (Use any method; show work

  • Answer: 23×15=(20×15)+(3×15)=300+45=34523×15=(20×15)+(3×15)=300+45=345
100

Write an expression for: "Add 8 and 7, then multiply the sum by 2." Then evaluate it.

  • Answer: 2×(8+7)=2×15=302×(8+7)=2×15=30
200

Use partial products to compute 127 × 4. List each partial product and the final total

  • Answer: (100×4)+(20×4)+(7×4)=400+80+28=508(100×4)+(20×4)+(7×4)=400+80+28=508
200

Without calculating fully, explain which is larger: 3 × (2,000) or 2 × (3,000). Then compute one to check.

  • Answer: They are equal; 3×2000=6000, 2×3000=60003×2000=6000, 2×3000=6000
200

 Evaluate: 3×(12+9)3×(12+9). Show one sentence explaining why parentheses change the result.

  • Answer: 3×(12+9)=3×21=633×(12+9)=3×21=63. Parentheses tell you to add first, then multiply.
300

Explain how place value influences the partial product when multiplying 203 × 5. Which digits give a zero partial product and why?

  • Answer: Tens digit is 0 so (0×5)=0(0×5)=0; partial products: (200×5)=1000, (0×5)=0, (3×5)=15 ⇒1015(200×5)=1000, (0×5)=0, (3×5)=15 ⇒1015
300

Multiply 412 × 23 using an area model or the partial products method and show your work

  • Answer: (400×20)+(400×3)+(12×20)+(12×3)=8000+1200+240+36=9476(400×20)+(400×3)+(12×20)+(12×3)=8000+1200+240+36=9476
300

Write an expression for: "Multiply 6 by the sum of 34 and 18." Then evaluate using partial sums where helpful.

  • Answer: 6×(34+18)=6×52=3126×(34+18)=6×52=312
400

Compute 46 × 38 using partial products (break each number by place value and show all partial products).

  • Answer: (40×30)+(40×8)+(6×30)+(6×8)=1200+320+180+48=1748(40×30)+(40×8)+(6×30)+(6×8)=1200+320+180+48=1748
400

A bakery makes 128 muffins per batch. How many muffins in 56 batches? Use partial products to solve.

  • Answer: (128×50)+(128×6)=6400+768=7168(128×50)+(128×6)=6400+768=7168
400

Which expression is equivalent to "5 times the sum of 48 and 2"? A) 5×48+25×48+2 B) 5×(48+2)5×(48+2) — explain and evaluate the correct one.

  • Answer: B. 5×(48+2)=5×50=2505×(48+2)=5×50=250. A equals 242, not equivalent.
500

A student multiplied 305 × 47 and forgot the partial product from the tens place of 47. Which partial product is missing? Show how it affects the final answer.

  • Answer: Missing (305×40)=12,200(305×40)=12,200; correct total: (305×7)=2135; 12,200+2,135=14,335(305×7)=2135; 12,200+2,135=14,335
500

Multiply 3,409 × 27 using partial products. Show each step and the final product

  • Answer: (3409×20)+(3409×7)=68,180+23,863=92,043(3409×20)+(3409×7)=68,180+23,863=92,043
500

Create a numerical expression (using parentheses) that equals 1,000 when evaluated and uses at least three operations. Show evaluation.

  • Sample Answer: (20+5)×40=25×40=1000(20+5)×40=25×40=1000
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